class TestStatisticDistribution:
def __init__(self, samples_x_y: SamplesXY,
shared_combined_sample: CombinedSample):
self.shared_combined_sample = shared_combined_sample
self.shared_combined_sample_size = self.shared_combined_sample.combined_sample_size
self.sample_size_y = samples_x_y.sample_size_y
self.sample_size_x = self.shared_combined_sample_size - self.sample_size_y
self.sample_size_x_y_gcd = gcd(self.sample_size_x, self.sample_size_y)
self.test_statistic_factor = self.sample_size_x * self.sample_size_y / self.sample_size_x_y_gcd
self.test_statistic_factor_approximate = self.sample_size_x_y_gcd / \
sqrt(self.sample_size_x * self.sample_size_y * self.shared_combined_sample_size)
self.algorithm = CountAlgorithm()
self.combined_sample_counts = []
self.x_meshing_cdf = []
self.y_meshing_cdf = []
self.max_cumulative_difference = 0
self.meshing_test_statistic = 0
self.y_item_positions = []
self.number_of_y_item_positions = 0
self.combined_sample_attributions_cache = []
self.distribution = Distribution()
def make_y_item_indices(self):
print("Calculating meshings... ", sep=" ", end=" ")
item_indices = [x for x in range(0, self.shared_combined_sample_size)]
self.y_item_positions = combinations(item_indices, self.sample_size_y)
self.number_of_y_item_positions = sum(1 for _ in self.y_item_positions)
# Restore the iterator
self.y_item_positions = combinations(item_indices, self.sample_size_y)
def get_y_item_positions(self):
return self.y_item_positions
def show_progress(self, step):
if step % 1000 == 0:
print("\rCalculating meshings... {}/{}".format(
step, self.number_of_y_item_positions),
sep=" ",
end=" ")
@staticmethod
def finish_progress():
print("\rCalculating meshings... Done")
def update_combined_sample_attributions(self, y_item_indices):
next_attributions = [
Source.FORM_SAMPLE_X
for _ in range(0, self.shared_combined_sample_size)
]
for index in y_item_indices:
next_attributions[index] = Source.FORM_SAMPLE_Y
self.shared_combined_sample.set_attributions(next_attributions)
def make_cdf_from_counts_x(self, count):
return Fraction(count, self.sample_size_x)
def make_cdf_from_counts_y(self, count):
return Fraction(count, self.sample_size_y)
def save_counts_as_x_meshing_cdf(self):
self.x_meshing_cdf = map(self.make_cdf_from_counts_x,
self.combined_sample_counts)
def save_counts_as_y_meshing_cdf(self):
self.y_meshing_cdf = map(self.make_cdf_from_counts_y,
self.combined_sample_counts)
def find_max_cumulative_difference(self):
cumulative_difference = []
for index, cumulative_probability_x_y in enumerate(
zip(self.x_meshing_cdf, self.y_meshing_cdf)):
cumulative_difference.append(
abs(cumulative_probability_x_y[0] -
cumulative_probability_x_y[1]))
self.max_cumulative_difference = max(cumulative_difference)
def calculate_test_statistic(self):
self.meshing_test_statistic = int(self.test_statistic_factor *
self.max_cumulative_difference)
def approximate_test_statistic(self):
self.meshing_test_statistic = self.test_statistic_factor_approximate * self.meshing_test_statistic
def append_test_statistic_to_distribution(self):
self.distribution.add_test_statistic(self.meshing_test_statistic)
def calculate_meshing_test_statistic(self):
self.count_x_in_combined_sample()
self.save_counts_as_x_meshing_cdf()
self.count_y_in_combined_sample()
self.save_counts_as_y_meshing_cdf()
self.find_max_cumulative_difference()
self.calculate_test_statistic()
def append_meshing_to_distribution(self):
self.calculate_meshing_test_statistic()
self.append_test_statistic_to_distribution()
def count_x_in_combined_sample(self):
self.algorithm.configure_count_x()
self.run_algorithm()
def count_y_in_combined_sample(self):
self.algorithm.configure_count_y()
self.run_algorithm()
def run_algorithm(self):
self.shared_combined_sample.run(self.algorithm)
self.combined_sample_counts = self.algorithm.get_combined_sample_counts(
)
def make_probabilities(self):
self.distribution.calculate_probabilities()
def make_test_statistic_distribution(self):
self.make_y_item_indices()
for index, y_item_indices in enumerate(self.get_y_item_positions()):
self.show_progress(index)
self.update_combined_sample_attributions(y_item_indices)
self.append_meshing_to_distribution()
self.finish_progress()
self.make_probabilities()
def make_test_statistic(self):
self.calculate_meshing_test_statistic()
def make_test_statistic_approximate(self):
self.calculate_meshing_test_statistic()
self.approximate_test_statistic()
def cache_attributions(self):
self.combined_sample_attributions_cache = self.shared_combined_sample.get_attributions_copy(
)
def restore_attributions(self):
self.shared_combined_sample.set_attributions(
self.combined_sample_attributions_cache)
def get_test_statistic(self):
return self.meshing_test_statistic
def get_probabilities(self):
return self.distribution.get_probabilities()
def get_calculate_p_values_for(self, observed_test_statistic):
p_value = 0
for test_statistic, probability in self.get_probabilities().items():
if test_statistic >= observed_test_statistic:
p_value += probability
return p_value
def perform_test(self):
# Get the value of the test statistic for the combined samples with the original attributions
self.make_test_statistic()
observed_value_of_test_statisitic = self.get_test_statistic()
self.cache_attributions()
# Make test statistic distribution
self.make_test_statistic_distribution()
p_value = self.get_calculate_p_values_for(
observed_value_of_test_statisitic)
self.restore_attributions()
print("Observed value of test statistic is {}".format(
observed_value_of_test_statisitic))
print("Exact p-value is {}\n".format(p_value))
def perform_test_approximate(self):
self.make_test_statistic_approximate()
observed_value_of_test_statisitic = self.get_test_statistic()
print("Observed approximate value of test statistic is {}".format(
observed_value_of_test_statisitic))
print("Critical value for 0.05-rejection region is 1.358\n")
